.
Angewandte
Communications
to 200 mm from the pump and at time points from 0 s to 7 s
after exposure to fluoride. There is a clear Gaussian
distribution of particle velocities at each concentration of
fluoride over this range of distances and time, yet the average
velocities of the particles increased as a function of the
concentration of fluoride, reaching an estimated maximum
velocity of 1.15 mmsꢀ1 at 0.1m NaF.
The effect of analyte concentration on pumping velocity
was observed with PECA pumps as well (Figure 3b), which
reached a maximum average pumping velocity of approx-
imately 11 mmsꢀ1 in a pH 14 aqueous solution (1m OHꢀ). This
velocity is approximately twice as fast as the average
swimming velocity of Escherichia coli (E. coli) (5–7 mmsꢀ1 at
surfaces[13]).
The pumping velocity for this type of pump, as with all
pumps, depends on the distance from the pump where the
velocity is measured. Figure 3c shows the change in average
particle velocity as a function of distance for a TBS-PPHA
pump over the time period of 5 s to 35 s after exposure to 0.1m
NaF at 258C. The data in Figure 3c reveals that the TBS-
PPHA pump is capable of providing average pumping
velocities of at least 0.8 ꢁ 0.4 mmsꢀ1 at distances over 1 mm
from the pump.
Figure 4. Proposed diffusiophoretic mechanism for enhanced rates of
diffusion of 2 mm PECA particles (maroon semi-spherical object) in
basic aqueous solutions. Note: As the particles degrade to some
extent over their entire surface creating multiple product sources, the
generated product gradient across the particle is not likely to be as
steep as that shown here in the idealized picture.
Our hypothesized mechanism for these pumps is depicted
in Figure 1. This mechanism is based on a non-electrolyte
diffusiophoretic model in which the concentration gradient of
monomeric products above the polymer film leads to move-
ment of water in the z direction from above the film towards
the film. This movement of water creates convective flow
within the confines of the test container that leads to the
movement of water initially in the z direction towards the
pump, and then radially away from the pump in the x,y plane.
To test this mechanism, we prepared 2 mm diameter
PECA particles (Supporting Information, Figure S1) as
a control system to evaluate whether analyte-induced depo-
lymerization would cause enhanced diffusion rates of the
PECA particles. Techniques for probing the mechanisms that
lead to motion of particles are well established,[14] therefore
we reasoned that control studies using PECA particles, rather
than films, might provide further insight into the mechanism
of the pumps.
creating a pressure gradient along the particle. This pressure
gradient drives fluid flow in the direction of higher product
concentration, thus pushing the particle in the opposite
direction. The depolymerization process is related to the
particle velocity (U) by the equation:[15,16]
kT
h
ð1Þ
U ¼
KLrC
where k is the Boltzmann constant, T is temperature, h is
viscosity, K is the Gibbs absorption length, L is the length of
the particle–product interaction, and C is the product
concentration. The observed enhanced diffusion coefficient
of the PECA particles in the presence of base can be related
to the ballistic velocity through the following equation:
U 2
4Dr
*
D ꢀD ¼
ð2Þ
The 2 mm-diameter PECA particles show enhanced
diffusivity (see Supporting Information) in basic solutions,
which we attribute to the depolymerization reaction and not
to the decrease in particle size that results over the course of
the depolymerization reaction. As depolymerization is an
endothermic, entropy-driven reaction, the enhanced diffusion
is not because of local heating. Instead, we propose that the
enhanced diffusivity arises from shape asymmetry and surface
imperfections in the particles that leads to greater exposure of
some areas on the particle to the analyte in solution
(Figure 4).
where D*ꢀD is the net enhancement in diffusion coefficient,
U is the particle velocity, and Dr is the rotational diffusion
coefficient (for a 2 mm particle Dr is calculated to be
0.23 sꢀ1).[14,17] Using the relationship described by Equa-
tion (2), the calculated velocity of the particles are
0.18 mmsꢀ1 in pH 8 solution and 0.25 mmsꢀ1 in pH 8.5
solution. These velocities compare well with the observed
pumping velocity for PECA pumps at pH 8 (0.21 ꢁ
0.12 mmsꢀ1). The agreement between the computed particle
velocity and the experimental pump velocities lead us to
conclude that the same mechanism probably causes both the
convective flow of water around the pumps and the enhanced
rate of diffusion of the PECA particles.
A larger area of exposure should lead to an increase in the
number of polymers that depolymerize, causing an uneven
increase in the local concentration of monomeric products
around the particle and an increased diffusivity owing to
a
non-electrolyte diffusiophoretic mechanism.[15,16] This
With an eye towards future applications, we broadened
the scope of these new types of autonomous pumps by
demonstrating the ability of TBS-PPHA pumps to move
mechanism arises from steric exclusion, which is generated
from the products interacting with the particle surface, thus
ꢀ 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2012, 51, 2400 –2404